Download OU B.Sc 2019 June-July 2nd Semester Mathematics Question Paper

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B.Sc. II-Semester (CBCS) Examination, May / Jun

Subject : Mathematics

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Paper - II : (Differential Equations)

Time : 3 Hours Max. Marks: 80

PART - A (5 x 4 = 20 Marks)

(Short Answer Type)

Note : Answer any FIVE of the following questions.

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1. Solve (1 + x²) dx + x(1 - xy) dy = 0
2. Solve x²p² + xyp - 6y² = 0
3. Solve d²y/dx² - 3dy/dx + 2y = 0 with y=0, x=0 and dy/dx = 0
4. Solve (D² -1)y = sin x.
5. Solve (D²-3D + 2) y = sine^x using variation of parameters.

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6. Solve x²y" - xy' +y =0 given y₁ = x as a solution.
7. Form a partial differential Equation from z = f(x²+ y²) eliminating arbitrary function f.
8. Solve (y-z)p+ (x-y)q=z-x.

PART - B (4 x 15 = 60 Marks)

(Essay Answer Type)

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Note: Answer ALL from the questions.

9. (a) Show that the necessary and sufficient condition for the differential equation Mdx + Ndy = 0 to be exact is that ?M/?y = ?N/?x
   OR
   (b) Solve y + px = x²p²
10. (a) Solve (D²+1)y = x cos x
    

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    OR
    (b) Solve (D²-2D+1)y=xe^x
11. (a) Solve x² d²y/dx² - 2x dy/dx - 3y=x²logx
    OR
    (b) Use method of undetermined coefficients to solve (D² - 3D +2)y = 2x² +3e^2x

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12. (a) Solve (x² - y² - z²)p + 2xyq = 2xz.
    OR
    (b) Integrate and hence obtain a solution of ?²z/?x?y +18xy² +5sin(2x - y) = 0

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